It is shown that explicitly broken scale symmetry is essential for dense skyrmion matter in hidden local symmetry theory. Consistency with the vector manifestation fixed point for the hidden local symmetry of the lowest-lying vector mesons and the dilaton limit fixed point for scale symmetry in dense matter is found to require that the anomalous dimension ($|{\gamma }_{G^2}|$) of the gluon field strength tensor squared ($G^2$) that represents the quantum trace anomaly should be $1.0\lesssim |{\gamma }_{G^2}|\lesssim 3.5$. The magnitude of $|{\gamma }_{G^2}|$ estimated here will be useful for studying hadron and nuclear physics based on the scale-chiral effective theory. More significantly, that the dilaton limit fixed point can be arrived at with ${\gamma }_{G^2}\ne 0$ at some high density signals that scale symmetry can arise in dense medium as an “emergent” symmetry.

• Received 27 December 2016
• Revised 13 March 2017

DOI:https://doi.org/10.1103/PhysRevD.97.094017